Scala analysis: supermagic10
A distributionally even scale in supermagic temperament, abacbacabc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 59.110 cents 59.110000 2: 85.690 cents 85.690000 3: 321.680 cents 321.680000 4: 380.790 cents 380.790000 5: 616.780 cents 616.780000 6: 643.360 cents 643.360000 7: 702.470 cents 702.470000 8: 938.460 cents 938.460000 9: 965.040 cents 965.040000 10: 1201.030 cents 1201.030000
SHOW/INTERVAL
0: 235.9900 cents 235.9900 1: 59.1100 cents 59.1100 2: 26.5800 cents 26.5800 3: 235.9900 cents 235.9900 4: 59.1100 cents 59.1100 5: 235.9900 cents 235.9900 6: 26.5800 cents 26.5800 7: 59.1100 cents 59.1100 8: 235.9900 cents 235.9900 9: 26.5800 cents 26.5800 10: 235.9900 cents 235.9900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 26.58000 cents 1: 3 59.11000 cents 1: 4 235.99000 cents 2: 2 85.69000 cents 2: 4 262.57000 cents 2: 4 295.10000 cents 3: 8 321.68000 cents 3: 1 498.56000 cents 3: 1 531.09000 cents 4: 2 348.26000 cents 4: 2 380.79000 cents 4: 6 557.67000 cents 5: 5 584.25000 cents 5: 5 616.78000 cents 6: 6 643.36000 cents 6: 2 820.24000 cents 6: 2 852.77000 cents 7: 1 669.94000 cents 7: 1 702.47000 cents 7: 8 879.35000 cents 8: 4 905.93000 cents 8: 4 938.46000 cents 8: 2 1115.34000 cents 9: 4 965.04000 cents 9: 3 1141.92000 cents 9: 3 1174.45000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.88889 = 26/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 59.1 85.7 321.7 380.8 616.8 643.4 702.5 938.5 965.0 1201.0 59.1 : 26.6 262.6 321.7 557.7 584.3 643.4 879.4 905.9 1141.9 1201.0 85.7 : 236.0 295.1 531.1 557.7 616.8 852.8 879.3 1115.3 1174.5 1201.0 321.7 : 59.1 295.1 321.7 380.8 616.8 643.4 879.4 938.5 965.0 1201.0 380.8 : 236.0 262.6 321.7 557.7 584.3 820.2 879.4 905.9 1141.9 1201.0 616.8 : 26.6 85.7 321.7 348.3 584.3 643.4 669.9 905.9 965.0 1201.0 643.4 : 59.1 295.1 321.7 557.7 616.8 643.4 879.3 938.5 1174.4 1201.0 702.5 : 236.0 262.6 498.6 557.7 584.3 820.2 879.3 1115.3 1141.9 1201.0 938.5 : 26.6 262.6 321.7 348.3 584.2 643.4 879.3 905.9 965.0 1201.0 965.0 : 236.0 295.1 321.7 557.7 616.8 852.8 879.4 938.5 1174.5 1201.0 1201.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.5800 .. 235.9900 cents 209.41000 cents 26.58000 cents 2: 85.6900 .. 295.1000 cents 209.41000 cents -150.30000 cents 3: 321.6800 .. 531.0900 cents 209.41000 cents 26.58000 cents 4: 348.2600 .. 557.6700 cents 209.41000 cents -182.83000 cents 5: 584.2500 .. 616.7800 cents 32.53000 cents 26.58000 cents 6: 643.3600 .. 852.7700 cents 209.41000 cents 26.58000 cents 7: 669.9400 .. 879.3500 cents 209.41000 cents -182.83000 cents 8: 905.9300 .. 1115.3400 cents 209.41000 cents 26.58000 cents 9: 965.0400 .. 1174.4500 cents 209.41000 cents -150.30000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 26.58000 cents, class 1 Average step (divided formal octave): 120.1030 cents Largest one step interval : 235.99000 cents Average / Smallest step : 4.518548 Largest / Average step : 1.964897 Largest / Smallest step : 8.878480 Median interval of one step : 59.11000 cents, amount: 3 Most common interval of one step : 235.99000 cents, amount: 4 Least squares average step : 111.12566 cents, oct.: 1111.25662 cents Scale is not proper Scale is 3-distributional even Step pattern alph. order: ABCACBACBC Step pattern size order : MSLMLSMLSL Scale is a Constant Structure, by a margin of 26.58000 cents Scale diversity : 1.193481 Lumma stability : 0.132786 Lumma impropriety factor : 0.554741 Rothenberg efficiency : 0.526429 redundancy: 0.473571 Efficiency x scale size : 5.264286 Number of different interval sizes : 26 = 2.88889 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.88889 = 26/9 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 26.58000 cents Most common intervals : 321.68000 cents & inv., amount: 8 Most common triad is 0.0 321.680 879.350 cents, amount: 6 Number of recognisable fifths : 1, average 702.4700 cents Number of recognisable fourths : 1, average 498.5600 cents Formal octave complements present : 1 = 10.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 8-9 -- Rational properties --
FIT/MODE
10: 0 1 2 0 2 0 1 2 0 2 N B D3 SD: 30.8827 c. M: 59.1100 c. 12: 1 0 2 1 2 0 1 2 1 2 N T3 SD: 27.4491 c. M: 42.8450 c. 13: 1 0 2 1 3 0 1 2 0 3 N SD: 27.2338 c. M: 44.5192 c. 14: 1 0 3 0 3 0 1 3 0 3 N T3 SD: 23.3130 c. M: 42.8450 c. 15: 1 0 3 1 3 0 1 3 0 3 N D3 SD: 15.0842 c. M:-23.7693 c. 19: 1 0 4 1 4 0 1 4 0 4 N D3 SD: 11.6072 c. M: 22.4779 c. 24: 1 1 4 2 4 1 1 5 0 5 N SD: 13.4371 c. M: 21.4225 c. 25: 1 1 5 1 5 0 2 5 0 5 N SD: 13.1081 c. M:-22.3640 c. 26: 1 1 5 1 5 1 1 5 1 5 N B DE S SD: 9.7278 c. M: 16.2650 c. 31: 2 0 6 2 6 1 1 6 1 6 N SD: 9.7086 c. M:-18.3758 c. 37: 2 1 7 2 7 1 2 7 1 7 N D3 SD: 7.1449 c. M:-11.6908 c. 41: 2 1 8 2 8 1 2 8 1 8 N D3 SD: 1.1559 c. M:-2.1902 c. 142: 7 3 28 7 28 3 7 28 3 28 N D3 SD: 0.5593 c. M: 1.1104 c. 183: 9 4 36 9 36 4 9 36 4 36 N D3 SD: 0.1879 c. M: 0.3709 c. 224: 11 5 44 11 44 5 11 44 5 44 N D3 SD: 0.1047 c. M: 0.1798 c. 407: 20 9 80 20 80 9 20 80 9 80 N D3 SD: 0.0858 c. M: 0.1478 c. 631: 31 14 124 31 124 14 31 124 14 124 N D3 SD: 0.0769 c. M: 0.1244 c. 855: 42 19 168 42 168 19 42 168 19 168 N D3 SD: 0.0792 c. M: 0.1133 c. 1038: 51 23 204 51 204 23 51 204 23 204 N D3 SD: 0.0782 c. M: 0.1336 c. 1359: 67 30 267 67 267 30 67 267 30 267 N D3 SD: 0.0741 c. M:-0.1193 c. 1400: 69 31 275 69 275 31 69 275 31 275 N D3 SD: 0.0767 c. M:-0.1326 c. 1542: 76 34 303 76 303 34 76 303 34 303 N D3 SD: 0.0603 c. M:-0.0914 c. 1583: 78 35 311 78 311 35 78 311 35 311 N D3 SD: 0.0534 c. M:-0.0908 c. 1766: 87 39 347 87 347 39 87 347 39 347 N D3 SD: 0.0406 c. M:-0.0577 c. 1807: 89 40 355 89 355 40 89 355 40 355 N D3 SD: 0.0402 c. M:-0.0694 c. 1949: 96 43 383 96 383 43 96 383 43 383 N D3 SD: 0.0380 c. M:-0.0651 c. 1990: 98 44 391 98 391 44 98 391 44 391 N D3 SD: 0.0263 c. M:-0.0420 c. 2173: 107 48 427 107 427 48 107 427 48 427 N D3 SD: 0.0233 c. M:-0.0398 c. 2214: 109 49 435 109 435 49 109 435 49 435 N D3 SD: 0.0170 c. M:-0.0295 c. 2397: 118 53 471 118 471 53 118 471 53 471 N D3 SD: 0.0113 c. M:-0.0193 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 1.0300 cents 2 x x x x x x 3 x x 4 S SD: 0.5758 cents 3 x x x 4 x x x 5 x 6 S SD: 43.0462 cents 4 x x x 5 x x 6 x 7:8 S SD: 1.6987 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 25.5680 cents 6 x x 7 x x x 9:10 x 12 SD: 19.2554 cents 7 x x 8:9:10 x 11:12 x 14 S SD: 22.0937 cents 8 x x x 10:11 x 12 x 14:16 S SD: 13.1628 cents 9 x 10:11 x x 13:14:15:16:18 SD: 19.0876 cents 10 x 11:12 x 14 x 15:17 x 20 SD: 14.8095 cents 11 x 12:13:14 x 16:17:19 x 22 SD: 13.7973 cents 12 x 13:14:15:17 x 18 x 21:24 SD: 11.0994 cents 13 x 14 x 16 x 19:20:22:23:26 SD: 10.7039 cents 14 x 15:17 x 20 x 21:24 x 28 SD: 6.1875 cents 15 x 16:18:19:21:22:23 x 26:30 SD: 8.5326 cents 16 x 17:19:20:23 x 24 x 28:32 SD: 4.8096 cents 17 x 18:20:21:24:25:26:29:30:34 SD: 7.5607 cents 18 x 19:22 x x 26:27:31 x 36 SD: 4.6501 cents 19 x 20:23:24:27:28:29 x 33:38 SD: 6.2086 cents 20 x 21:24:25 x 29:30:34:35:40 SD: 2.7298 cents 21 x 22:25:26:30 x 32:36:37:42 SD: 4.8867 cents 22 x 23:26:27:31:32:33:38 x 44 SD: 6.1754 cents 23 x 24:28:29:33 x 35 x 40:46 SD: 5.7745 cents 24:25 x 29:30:34:35:36:41:42:48 SD: 2.7899 cents 25:26 x 30:31 x 36:38:43:44:50 SD: 3.9920 cents 26:27 x 31:32:37:38:39:45 x 52 SD: 4.2147 cents 27:28 x 33:34 x 39:41:46:47:54 SD: 5.2657 cents 28:29 x 34:35:40:41:42:48:49:56 SD: 2.6560 cents 29:30 x 35:36:41:42:44:50:51:58 SD: 3.3432 cents 30:31:32:36:37:43:44:45 x 52:60 SD: 4.4833 cents 31:32:33:37:39:44:45:47:53:54:62 SD: 3.9944 cents 32:33:34:39:40:46 x 48:55:56:64 SD: 3.5433 cents 33:34:35:40:41:47:48:50:57:58:66 SD: 3.1508 cents 34:35:36:41:42 x 49:51:58:59:68 SD: 3.3502 cents 35:36:37:42:44:50:51:53:60:61:70 SD: 2.9240 cents 36:37:38:43:45:51:52:54:62:63:72 SD: 2.6184 cents 40:41:42:48:50:57:58:60:69:70:80 SD: 1.9868 cents 41:42:43:49:51 x 59:62:71:72:82 SD: 3.6790 cents 42:43:44:51:52:60:61:63:72:73:84 SD: 2.8234 cents 44 x 46:53:55:63:64:66:76:77:88 SD: 1.6937 cents 45 x 47:54:56:64:65:68:77:79:90 SD: 2.6162 cents 46 x 48:55:57:66:67:69:79:80:92 SD: 2.6521 cents 47:49 x 57:59:67:68:71:81:82:94 SD: 2.8678 cents 48:50 x 58:60:69:70:72:83:84:96 SD: 2.5738 cents 49:51 x 59:61:70:71:74:84:86:98 SD: 2.0518 cents 53:55:56:64:66:76:77:80:91:93:106 SD: 1.9781 cents 54:56:57:65:67:77:78:81:93:94:108 SD: 1.4874 cents 58:60:61:70:72:83:84:87:100:101:116 SD: 1.1087 cents 78:81:82:94:97:111:113:117:134:136:156 SD: 1.0079 cents 82:85:86:99:102:117:119:123:141:143:164 SD: 0.7686 cents 114:118:120:137:142:163:165:171:196:199:228 SD: 0.6312 cents 118:122:124:142:147:169:171:177:203:206:236 SD: 0.5728 cents 122:126:128:147:152:174:177:183:210:213:244 SD: 0.5306 cents 138:143:145:166:172:197:200:207:237:241:276 SD: 0.4173 cents 142:147:149:171:177:203:206:213:244:248:284 SD: 0.3746 cents 196:203:206:236:244:280:284:294:337:342:392 SD: 0.3249 cents 236:244:248:284:294:337:342:354:406:412:472 SD: 0.2600 cents 260:269:273:313:324:371:377:390:447:454:520 SD: 0.2222 cents 318:329:334:383:396:454:461:477:547:555:636 SD: 0.2116 cents 378:391:397:455:471:540:548:567:650:660:756 SD: 0.1860 cents 456:472:479:549:568:651:661:684:784:796:913 SD: 0.1737 cents 489:506:514:589:609:698:709:734:841:854:979 SD: 0.1733 cents 495:512:520:596:617:707:718:743:851:864:991 SD: 0.1730 cents 516:534:542:621:643:737:748:774:887:901:1033 SD: 0.1712 cents 549:568:577:661:684:784:796:824:944:959:1099 SD: 0.1167 cents